摘要
引入Hawkes过程来代替经典的泊松过程,建立了索赔具有族群特性的一类保险公司分红模型,并探究了最优分红策略问题.引入粘性解的概念,利用动态规划原理推导出优化问题,其解满足一个完全非线性偏微分方程:Hamilton-Jacobi-Bellman方程,并证明了值函数是相关方程的粘性解,给出了验证定理.最后进行数值模拟实验,并介绍了障碍线策略实施过程.
The optimal dividend payment problem in an insurance company whose surplus follows the classical Cramér-Lundberg process with cluster claims is considered.A Hawkes process is introduced so that the occurrence of a claim in the risky asset price triggers more sequent jumps.Using dynamic programming principle and viscosity solution theory,it shows that the optimal value function is a viscosity solution of the associated Hamilton-Jacobi-Bellman(HJB)equation.The optimal value function can be characterized as the smallest viscosity supersolution of the HJB equation.Finally,some numerical results are exhibited and a barrier line strategy is introduced.
作者
陈亦令
边保军
CHEN Yi-ling;BIAN Bao-jun(School of Mathematical Sciences,Tongji University,Shanghai 200092,China)
出处
《高校应用数学学报（A辑）》
北大核心
2020年第2期158-168,共11页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
国家自然科学基金(11771135)。
关键词
保险
最优分红
Hawkes过程
粘性解
障碍线策略
insurance
optimal dividend payment
Hawkes process
viscosity solution
barrier line strategy
